To start understanding music theory, it is helpful to study the building blocks that we can use to analyze, compose and improvise. Fancy words like “Music theory” or “Jazz improvisation” can be a little intimidating to many people, but with a little bit of work, anyone can learn some fundamentals that can be used to grow as a musician. That said, I will assume in these articles that you know how to read music sheet on treble clef. It will also be helpful that you keep a keyboard close, since it is the most graphic way to study theory, but if that is not possible, at least try to keep your instrument at hand to follow along.

These articles are going to be loosely based on a similar series I wrote in Spanish some years ago under the silly pseudonym of Aiden Fox. If you are interested on those, you can find them at Cutaway Magazine issues #24 and #25.

Intervals

In Western tonal music, we divide the different instrument ranges in a 12 note scale separated by the minimum unit of a half step. These notes, when arranged sequentially form the chromatic scale.

From this scale we can derive any number of major, minor or exotic scales. Furthermore, we are going to start looking at the intervals. A simple definition for “iterval” would be the difference between two pitches or the distance that exists between two of the notes of the chromatic scale. The notes of an interval could be played in unison, in ascending form and descending form.

To simplify the explanations we are going to look only at unison intervals, being the ones in ascending form those where the lowest pitch is played before the highest one and vice versa for the descending form. In the following figure you can see all possible intervals within a octave, starting at a half step and moving half step at a time towards the six steps that give us an octave.

Typically you will see a different nomenclature to refer to these intervals, in the same order:

1 - b2 - 2 - b3 - 3 - 4 - b5 - 5 - #5 - 6 - b7 - 7

Larger intervals, like the 9th, the 11th or the 13th, are also possible but it is nothing more than a 2nd, 4th or 6th interval one octave above.

Intervals can also be inverted. To do this, we will put the lowest note one octave higher or the other way around. Without going into too much detail here is what this implies:

Major becomes minor and vice versa.

Diminished becomes augmented and vice versa.

Perfect intervals remain perfect.

A tritone remains a tritone.

Knowing the intervals it is extremely useful when we are trying to transpose a song, compose our own pieces or make arrangements to existing ones.

It will be really good if we could identify by ear the different intervals. This is a skill that can be trained, allowing us to rapidly transcript a passage or improvise over it. One of the most effective ways to educate ourselves for this is to try to associate different intervals to well known songs that are already stuck in our heads: The Jaws main theme starts with a minor 2nd, while Happy Birthday starts with a major second.

Triads

Different intervals can be grouped to obtain different textures and try to evoke an emotional response on the listener. The most common way to group intervals is by creating triads joining major and minor 3rds. We can classify triads in major, minor, augmented and diminished. Triads an be inverted twice in the same way as two note intervals.

More precisely, a triad is a chord formed by the root, the 3rd and the 5th. In other words, a combination of the interval from the root to the 3rd and the interval from the root to the fifth. This is equivalent to two thirds stack on top of each other.

In the previous example it could be seen very clearly how the C major triad it is made by stacking a C to E major 3rd interval with a E to G minor 3rd interval. That said, the way we can compose the 4 main triads is: